Many different transmission schemes may be used to transmit signals, for example over wireless or wired transmission systems. Some transmission schemes use frequency-division multiplexing (e.g. orthogonal frequency-division multiplexing (OFDM)), whereby a transmitted signal comprises a sequence of symbols which are transmitted over time, wherein each symbol comprises a plurality of distinct data slots for transmitting data using a respective plurality of subcarriers which are distinct in the frequency domain.
Signals are transmitted over a channel from a transmitter to a receiver. The channel will affect the signal, such that the signal transmitted from the transmitter is not the same as the signal received at the receiver. A channel impulse response (CIR) describes the effect that the channel will have on the signal, e.g. as a function of time. In particular, the CIR is the signal that would be received at the receiver if an instantaneous pulse (or “impulse”) is transmitted from the transmitter. If the receiver can determine the CIR then the receiver will usually be able to more accurately decode the symbols in the received signal because the receiver can take into account the effect of the channel on the received signal.
In order for the receiver to determine the CIR, pilot signals are transmitted from the transmitter over the channel to the receiver. That is, some of the sub-carriers in some of the symbols carry pilot signals for measurement of the channel conditions. The receiver knows the characteristics (e.g. spectral shape) of the pilot signals that the transmitter will transmit, so by comparing the characteristics of the received pilot signals to the known characteristics of the pilot signals, the receiver can determine the effects of the channel on the pilot signals, thereby determining the CIR for the received signal. The pilot signals are applied to data slots of different symbols using different subcarriers in accordance with a pilot transmission scheme which is known to both the transmitter and the receiver. The transmission of a pilot signal in a data slot usually means that data cannot be transmitted in that data slot. Therefore, some systems reduce the number of pilot signals that are transmitted by making the assumption that the transmission channel is static in time for a number of symbols. With this assumption, the pilot signals can be applied to a sparse set of different subcarriers on different symbols such that over a range of symbols they will sound the channel with a sufficiently small frequency sampling interval that they can represent a channel with a suitable delay spread.
However, if the underlying assumption that the channel is static is not true then making this assumption may lead to distortion in the estimated channel impulse response when the pilot signals are considered from multiple symbols. The resulting distortion in the CIR may degrade processes at the receiver, such as equalization and tracking, which use the CIR.